-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -2, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 1, 'Lhash': '1554562899595883463', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 712.5211073162894, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [11, [1, -1]], [13, [1]]], 'bad_primes': [2, 3, 11, 13], 'central_character': '89232.1', 'coefficient_field': '1.1.1.1', 'conductor': 89232, 'conductor_radical': 858, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 2, 5], [1, 2, 7], [1, -1], [1], [1, -4, 17], [1, 6, 19], [1, 0, 23], [1, 8, 29], [1, 8, 31], [1, 10, 37], [1, 8, 41], [1, -2, 43], [1, 8, 47], [1, 2, 53], [1, -12, 59], [1, -10, 61], [1, -12, 67], [1, -8, 71], [1, 6, 73], [1, -2, 79], [1, -16, 83], [1, -14, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 25, 'label': '2-89232-1.1-c1-0-25', 'leading_term': '2.94769905398', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/89232/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.5840992856301974, 0.335945658508952, -1.062972712630631, -2.870791192259458, -3.513857850043001, -2.048771437675022, 0.3744855853012462, 1.084773982764614, -1.346607658030415, -5.030257094834164, -6.353306679274372, -4.033661549100148, -0.6953769484303663, 0.4811702968932372, -0.1400302386978341, 0.4124796401402723, 2.865998248831105, 4.208988168607274, 2.261651029515391, -0.537043895344822, -0.5005373596680998, 1.584623608977039, 1.658961659433315, -0.9905794965704914, -2.504951039282717, -0.9320313918103244, 0.5159912959980149, -0.7263444005268908, -1.828699327922725, 0.2538235897859239, 2.667975949735359, 1.309353829226977, -1.388128694657423, -0.1580704083345009, 3.499773462758832, 3.343778110234068, -0.6332134328990778, -1.970073768554956, 0.8632438080173196, 2.077396061021127, -0.5344903247969631, -1.829531862576262, 0.6009732942830385, 2.121771369221644, 0.415312203861446, -0.358926146556451, 1.517366874291789, 1.922361734516394, -0.1722737849627641, -0.5008014037222596, 1.086762916140835, 0.1196204146425934, -1.82434899780076, 1.406229938899379, 7.208469154634023, 6.506170119285968, 0.1144809216908801, -2.297285497687925, 0.4839281514452051, 0.8710815392454667, -1.716515382175399, -1.091426450367494, 1.901462632649285, 1.617153664270866, -0.3841788535678193, 0.1133877320503176, 0.2595423158837523, -2.440009580590694, -3.062569547044332, -0.2318056113734576, -0.8618113692337872, -5.754747248701516, -6.456285665792218, -1.713645068510747, 0.6703641707753779, -0.2893659298327675, 0.4342171657176705, 0.6735824828454304, -3.015551519523666, -4.690504059628281, -0.8669560184007056, 0.5899034100197391, -3.136669429103742, -3.103615429182816, 2.244407067248815, 3.336523586011051, -0.5247703534430791, -0.8229383606333275, 1.782703763278003, 1.006916759412894, -0.5728146402317107, 0.8390824373726796, 1.222886407705785, -0.4087263966214351, 0.3461225222416664, 1.032426889271044, -2.236958943499061, -2.902403036064937, 2.592406517871149, 4.466194363734291, -0.7568115879047346, -2.854935804875689, -0.02121377895085064, -0.7518729598833687, -2.630218729023179, 1.767282775416818, 6.123118923654235, 3.233956513414006, -0.2245945502334404, 0.4279459476436582, 0.2488146249830402, -0.243369915509295, 2.591567407415337, 3.312158375979646, -0.7027577781755852, -1.534893444062692, 1.587384570633837, 1.081935526969541, -0.7860447960081471, 1.041275755380449], 'positive_zeros': ['0.5805066102372999', '1.706679487599166', '2.146196650675746', '3.331625935898923', '3.694685653246139', '3.926771317051120', '4.937035031155925', '5.314927475946371', '5.916232717756071', '6.612537544988117', '6.902407113849555', '7.479797735605734', '8.103102288694718', '8.511284175067852', '9.209746791396241', '9.684294167689569', '10.20694311894262', '10.70038381909452', '11.30382652191058', '11.56711952164505', '12.22844281975795', '12.57815227298574', '13.01170753875220', '13.43578243790896', '14.25496466858539', '14.70898811256918', '15.08600481511800', '15.58586227300791', '16.18067940055027', '16.47780206350091', '16.78524974774392', '17.52807401748547', '17.67610661403522', '18.61237189461200', '18.92340964178042', '19.17649684829858', '19.56551374174806'], 'prelabel': '2-89232-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 26.69309100340928, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1554562899595883463, 'z1': {'__RealLiteral__': 0, 'data': '0.5805066102372999', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.706679487599166', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.146196650675746', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 712.5211073162894, 'bad_primes': [2, 3, 11, 13], 'central_character': '1.1', 'conductor': 89232, 'conductor_radical': 858, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -2, 0, -2, 0, 1, 0, 1, 0, 0, 0, 2, 0, 4, 0, -6, 0, 2, 0, 0, 0, -1, 0, -1, 0, -8, 0, -8, 0, -1, 0, 4, 0, -10, 0, 0, 0, -8, 0, 2, 0, -2, 0, -8, 0, -3, 0, -4, 0, -2, 0, -2, 0, 6, 0, 12, 0, 10, 0, -2, 0, 0, 0, 12, 0, 0, 0, 8, 0, -6, 0, 1, 0, -2, 0, 2, 0, 1, 0, 16, 0, -8, 0, 8, 0, 14, 0, 0, 0, 8, 0, 12, 0, 2, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, 0, 0], 'euler17': [1, -4, 17], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 8, 29], 'euler3': [1, 1, 0], 'euler31': [1, 8, 31], 'euler37': [1, 10, 37], 'euler41': [1, 8, 41], 'euler43': [1, -2, 43], 'euler47': [1, 8, 47], 'euler5': [1, 2, 5], 'euler53': [1, 2, 53], 'euler59': [1, -12, 59], 'euler61': [1, -10, 61], 'euler67': [1, -12, 67], 'euler7': [1, 2, 7], 'euler71': [1, -8, 71], 'euler73': [1, 6, 73], 'euler79': [1, -2, 79], 'euler83': [1, -16, 83], 'euler89': [1, -14, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 2, 5], [1, 2, 7], [1, -1, 0], [1, 0, 0], [1, -4, 17], [1, 6, 19], [1, 0, 23], [1, 8, 29], [1, 8, 31], [1, 10, 37], [1, 8, 41], [1, -2, 43], [1, 8, 47], [1, 2, 53], [1, -12, 59], [1, -10, 61], [1, -12, 67], [1, -8, 71], [1, 6, 73], [1, -2, 79], [1, -16, 83], [1, -14, 89], [1, -2, 97]], 'index': 25, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/89232/e'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-89232-1.1-c1-0-25', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-89232-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 26.69309100340928, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1554562899595883463, 'z1': {'__RealLiteral__': 0, 'data': '0.5805066102372999', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1554562899595883463', 'Lhash_array': ['1554562899595883463'], 'label': '2-89232-1.1-c1-0-25', 'type': 'ECQ', 'url': 'EllipticCurve/Q/89232/e'}